I feel like I've stuffed my stomach with a pork-flavoured duvet. I am at Subway in Camden high street, north London, and I have just shovelled down a foot-long sandwich called a Meatball Marinara. It is enormous. Laced with some sort of red sauce, the Marinara is filled with chunks of mince and slices of melted cheese – and wrapped in a baguette that disintegrates in your hands. My belly is throbbing like a highly charged cattle prod.

My experience is clearly not being shared by the public at large, though. The cashier in Camden tells me the Marinara is the shop's second-most popular sarnie, after the BMT (Biggest, Meatiest, Tastiest, which is filled with pepperoni, salami and ham). This week, it was announced that Subway has overtaken McDonald's as the largest fast-food chain on the planet. The sandwich company has 33,749 restaurants to the burger giant's 32,737, a lead of more than a thousand. In the UK, it's a similar picture: not only was Subway the country's most successful sandwich seller in 2010, but the company has more stores on these shores – 1,350 – than any of its fast-food rivals, including McDonald's.

In 2000, the chain only had 25 outlets in Britain – so how, and why, did Subway so quickly rein in McDonald's, for so long the symbol of global capitalism? One answer is a change in its business strategy. For many years, Subway focused its efforts on north America – where it was founded in 1965 by then high-school student Fred DeLuca, who had no background in fast food, but who wanted to raise money for college. This all changed in the last decade, when Subway realised it was missing out on a huge international market. "A population of 60 million indicates there are many [British] consumers who have not yet tried their first Subway sandwich," DeLuca ominously told the Guardian in 2005 – a situation I imagine he hopes has almost been rectified.

Subway's success is also down to the way its low-cost franchise model has proved attractive to local investors. "That's a huge part of the secret," says Trevor Haynes, who, as area development manager, heads up Subway's UK operations. "Our restaurants aren't company-owned: they're franchise-owned. We've attracted entrepreneurs who've enjoyed taking control of their own destiny." Though all Subways must be laid out the same (with limited seating and gloomy lighting, it appears), the franchise-owner has full control of their outlet's recruitment strategies, local promotions and opening hours.

For the punters in the street, Subway's appeal is three-fold. First, it's inexpensive. "It's a bigger option than Pret, and it's a lot cheaper," says Tom, 23, a publisher who works locally. "I come here for the sub of the day, it's just £2.29." For Wayne, 20, who works in a pet shop, Subway's draw is in the variety it offers to customers. "There's so much on offer," he tells me – and he'd be right. You have a choice of four breads, and scores of different meats, cheeses, sauces and salads. "I think if you worked out all the total combinations," claims Haynes, "there's a couple of million of them." James, 19, Wayne's reticent friend, has a third reason to eat at the chain: "Other [fast-food] places don't sell sandwiches, so it's much healthier."

Subway is often seen as the healthy fast-food chain because its primary product, the sandwich, seems so much more virtuous than a burger – and perhaps Subway itself, with its slogan "Eat Fresh", likes to play up that perception. But it's a bit of a moot point. "You think it's a healthier option," says Tom. "But what is 'healthy'?" Perhaps not his six-inch Meatball Marinara, which contains more than 500 calories and 11 grams of saturated fat – more than half of his recommended daily intake. Which means my own foot-long Marinara, twice the size, has presumably endowed me with more than 1,000 calories.

But, Haynes argues, at least this nutritional information is listed on the counter, and, besides, much of what Subway sells is genuinely low-fat. The Veggie Delite Salad and the Turkey Breast Wrap contain little in the way of calories or saturated fat. It was partly through eating meals like these that obese American student Jared Fogle famously lost 245 pounds in the late 90s, on a crash diet that saw him become the face of Subway advertising. He survived on a daily diet of coffee for breakfast, a six-inch turkey sub for lunch, and a foot-long veggie sub for dinner. "If you've not been behaving, you can eat something very, very healthy like a salad," says Haynes. "Or if you want to treat yourself, you can have something with triple cheese."

Helen Riley, a nutritional scientist from the British Nutritional Foundation, agrees, to a point. "Foods produced by any fast-food chain that are high in fat or sugar should just be eaten occasionally," says Riley. "They certainly shouldn't be eaten every day." With my stomach still churning the morning after the foot-long Meatball Marinara, I would certainly agree.